Re: Infinity

From: Mukul Gandhi <gandhi.mukul@gmail.com>
To: Michael Kay <mike@saxonica.com>
Date: Tue, 6 Mar 2018 11:21:36 +0530

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On Sat, Mar 3, 2018 at 2:52 PM, Michael Kay <mike@saxonica.com> wrote:

A question of no practical relevance for those on the list who are more mathematically inclined than I am.

From XSD 1.1 part 2 §3.3.13

(a) The ·value space· of integer is the infinite set {...,-2,-1,0,1,2,...}.

(b) integer has a lexical representation consisting of a finite-length sequence of decimal digits (#x30-#x39) with an optional leading sign.

So the value space is infinite, but the lexical space is finite. Or is it? Perhaps the set of finite-length strings is itself infinite?

Does every integer in this infinite set have a finite-length lexical representation? Or are there integers in the value space that have no representation in the lexical space?

Whenever I read this, I think, why is that adjective "finite-length" there? Would I have to change my software if it were removed?

I think, Mike's been pondering over this issue, although he knows his software (Saxon) is right (and I do as well). Mathematicians and scientists some times have these doubts.

I think, when a processor like that for XSD 1.1 is made with java language (as in case of Mike I think), we use underlying implementations of java.lang.Integer, or the primitive "int" to implement respectively xs:integer.

Regards,

Mukul Gandhi

Follow-Ups:
- Re: Infinity
  - From: Amelia A Lewis <amyzing@talsever.com>

References:
- Infinity
  - From: Michael Kay <mike@saxonica.com>

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